自适应笛卡尔网格超声速黏性流动数值模拟

doi:10.7527/S1000-6893.2017.21697

流体力学与飞行力学

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自适应笛卡尔网格超声速黏性流动数值模拟

唐志共, 陈浩, 毕林, 袁先旭

中国空气动力研究与发展中心计算空气动力研究所, 绵阳 621000

收稿日期:2017-08-28 修回日期:2017-11-17 出版日期:2018-05-15 发布日期:2017-11-17
通讯作者: 陈浩,E-mail:974257220@mail.qq.com E-mail:974257220@mail.qq.com
基金资助:
国家自然科学基金（11372341，91216203）

Numerical simulation of supersonic viscous flow based on adaptive Cartesian grid

TANG Zhigong, CHEN Hao, BI Lin, YUAN Xianxu

Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China

Received:2017-08-28 Revised:2017-11-17 Online:2018-05-15 Published:2017-11-17
Supported by:
National Natural Science Foundation of China (11372341, 91216203)

摘要/Abstract

摘要： 复杂外形/流场的高质量网格的生成往往需要占用大量人力资源，而自适应笛卡尔网格方法能够自动化生成高质量网格，具有很好的工程实用价值和应用前景。基于笛卡尔网格方法，采用叉树数据结构进行数据的存储和访问，分别从几何特征和流场解特征出发进行网格的自适应加密和粗化，发展了一种二维情况下自动、高效的自适应笛卡尔网格生成方法。从浸入边界方法出发，结合虚拟镜像对称方法和曲率修正技术进行黏性物面边界条件的处理，同时建立了多值点问题的处理技术，发展了一种在笛卡尔网格下可有效模拟黏性物面边界条件的方法。针对自适应笛卡尔网格非均匀的特点，发展了悬挂网格的处理方法，并构建了适用于自适应笛卡尔网格的黏性数值求解器。通过典型算例的考核，验证了所发展的自适应笛卡尔网格生成技术和构建的数值求解器具有较高的精度和可靠性。

关键词: 自适应笛卡尔网格, 叉树数据结构, 浸入边界方法, 黏性边界条件, 黏性数值求解器

Abstract: In comparison with the structured and the unstructured grids, the adaptive Cartesian grid can generate grid of high quality automatically, and has the application prospect in reducing manual labor. An adaptive Cartesian grid generation methodology with automation and efficiency under the two-dimensional condition is developed in this paper. The quadtree data structure is used for grids storage, making it trivial to accomplish grid adaptation. The grids are coarsened or refined based on the geometric features and solution for the flow field. The curvature corrected symmetry technique combined with the immersed boundary method is adopted to deal with the viscous boundary condition, achieving good results in computation of the viscous flow. A method for handling the multi-valued grids near thin surfaces and sharp corners is also developed. Considering the adaptive Cartesian grid is non-uniform, a processing method is developed for the hang-grid problem. Meanwhile, a viscous numerical solver applicable to the adaptive Cartesian grid is constructed. Typical simulation examples show the feasibility and reliability of the adaptive Cartesian grid generation methodology and the numerical solver.

Key words: adaptive Cartesian grid, quadtree data structure, immersed boundary method, viscous boundary condition, viscous numerical solver

中图分类号:

V211.3

唐志共, 陈浩, 毕林, 袁先旭. 自适应笛卡尔网格超声速黏性流动数值模拟[J]. 航空学报, 2018, 39(5): 121697-121697.

TANG Zhigong, CHEN Hao, BI Lin, YUAN Xianxu. Numerical simulation of supersonic viscous flow based on adaptive Cartesian grid[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(5): 121697-121697.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

自适应笛卡尔网格超声速黏性流动数值模拟

Numerical simulation of supersonic viscous flow based on adaptive Cartesian grid

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